Answer to Question #272317 in Molecular Physics | Thermodynamics for Nbj

Question

Q5. A 5 kg of ice cube at -10°C is mixed with 0.1 kg of water at 80 °C. There is no heat

loss to the surrounding. The specific heat capacity of ice is 2.22 kJK-1kg ? The specific

heat capacity of water is 4.187 kJK-kg“The specific latent heat of fusion of ice is

333 kJ kg-1

(a) What is the final physical state of the mixture? (Gas, Liquid or Solid?)

Justify your answer using suitable calculations

(b) What is the final temperature of the mixture?

Answer 1

a)

$Q_{i_{tot}}=c_im_i(0-t_i)=111~kJ,$

$Q_{w_{tot}}=c_wm_w(t_w-0)=33.5~kJ,$

$Q_{i_{tot}}>Q_{w_{tot}},$ it will be an ice,

b)

$Q_i=Q_{w_{tot}}+Q_{w_{\lambda}}+Q_{w_i},$

$c_im_i(t-t_i)=c_wm_w(t_w-0)+\lambda m_w+c_im_w(0-t),$

$t=\frac{m_w(\lambda+c_wt_w)+c_im_it_i}{c_i(m_i+m_w)}=-3.9°C.$